
Then, the CDF \({F_{\left. {{X_k}} \right|{{\bf {R}}_r}^{1/2}{\bf {Q}}{{\bf {R}}_r}^{1/2}}}\left( y \right)\)  can be derived by invoking inverse Laplace transform as[1]}
\({F_{\left. {{X_k}} \right|{{\bf {R}}_r}^{1/2}{\bf {Q}}{{\bf {R}}_r}^{1/2}}}\left( x \right) \\= {{\cal L}^{ - 1}}\left\lbrace  \frac{{{\mathcal {M}_{\left. {{X_k}} \right|{{\bf {R}}_r}^{1/2}{\bf {Q}}{{\bf {R}}_r}^{1/2}}}}\left( { - s}\right)}{s} \right\rbrace \left( x \right).\) 
